ABSTRACT

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

chapter 1|40 pages

The Algebra and Topology of ℝ n

chapter 2|39 pages

Differentiation

chapter 3|53 pages

Integration

chapter 4|43 pages

Change of Variables

chapter 5|40 pages

Manifolds

chapter 6|56 pages

Differential Forms

chapter 7|48 pages

Stokes’ Theorem

chapter 8|22 pages

Closed Forms and Exact Forms

chapter 9|13 pages

Epilogue-Life Outside ℝ n